Question

A thin target of ⁴⁸Ca with 1.3×10¹9 nuclei per cm² is bombarded with a 10 nA beam of α particles. A detector, subtending a solid angle of 2×10⁻³ steradians, records 15 protons per second. If the angular distribution is measured to be isotropic, determine the total cross section for the ⁴⁸Ca(α, p) reaction.

Answer 1

σ(total) = (Total number of particles scattered/sec)/((beam intensity) (number of target particles within the beam))

As the scattering is assumed to be isotropic total number of particles scattered 

= (Observed number) (4π/dΩ) = 15 × 4π/2 × 10⁻³ = 9.42 × 10⁴/s 

Beam intensity, that is number of beam particles passing through unit area per second